Severity: Warning
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Filename: drivers/Session_files_driver.php
Line Number: 177
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File: /var/www/html/index.php
Line: 316
Function: require_once
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Message: session_start(): Failed to read session data: user (path: /var/lib/php/sessions)
Filename: Session/Session.php
Line Number: 137
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File: /var/www/html/index.php
Line: 316
Function: require_once
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Message: Undefined array key "choices"
Filename: controllers/Detail.php
Line Number: 249
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File: /var/www/html/application/controllers/Detail.php
Line: 249
Function: _error_handler
File: /var/www/html/index.php
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Function: require_once
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Message: Trying to access array offset on value of type null
Filename: controllers/Detail.php
Line Number: 249
Backtrace:
File: /var/www/html/application/controllers/Detail.php
Line: 249
Function: _error_handler
File: /var/www/html/index.php
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Function: require_once
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Message: Trying to access array offset on value of type null
Filename: controllers/Detail.php
Line Number: 249
Backtrace:
File: /var/www/html/application/controllers/Detail.php
Line: 249
Function: _error_handler
File: /var/www/html/index.php
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Function: require_once
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Message: Trying to access array offset on value of type null
Filename: controllers/Detail.php
Line Number: 249
Backtrace:
File: /var/www/html/application/controllers/Detail.php
Line: 249
Function: _error_handler
File: /var/www/html/index.php
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Function: require_once
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Message: strpos(): Passing null to parameter #1 ($haystack) of type string is deprecated
Filename: models/Detail_model.php
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File: /var/www/html/application/models/Detail_model.php
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Function: strpos
File: /var/www/html/application/controllers/Detail.php
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Function: insertAPISummary
File: /var/www/html/index.php
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Function: require_once
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Message: str_replace(): Passing null to parameter #3 ($subject) of type array|string is deprecated
Filename: helpers/my_audit_helper.php
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File: /var/www/html/application/helpers/my_audit_helper.php
Line: 8919
Function: str_replace
File: /var/www/html/application/controllers/Detail.php
Line: 255
Function: formatAIDetailSummary
File: /var/www/html/index.php
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Function: require_once
Severity: Warning
Message: Undefined array key "choices"
Filename: controllers/Detail.php
Line Number: 256
Backtrace:
File: /var/www/html/application/controllers/Detail.php
Line: 256
Function: _error_handler
File: /var/www/html/index.php
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Function: require_once
Severity: Warning
Message: Trying to access array offset on value of type null
Filename: controllers/Detail.php
Line Number: 256
Backtrace:
File: /var/www/html/application/controllers/Detail.php
Line: 256
Function: _error_handler
File: /var/www/html/index.php
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Function: require_once
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Message: Trying to access array offset on value of type null
Filename: controllers/Detail.php
Line Number: 256
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File: /var/www/html/application/controllers/Detail.php
Line: 256
Function: _error_handler
File: /var/www/html/index.php
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Function: require_once
Severity: Warning
Message: Undefined array key "usage"
Filename: controllers/Detail.php
Line Number: 257
Backtrace:
File: /var/www/html/application/controllers/Detail.php
Line: 257
Function: _error_handler
File: /var/www/html/index.php
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Function: require_once
Severity: Warning
Message: Trying to access array offset on value of type null
Filename: controllers/Detail.php
Line Number: 257
Backtrace:
File: /var/www/html/application/controllers/Detail.php
Line: 257
Function: _error_handler
File: /var/www/html/index.php
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Function: require_once
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Message: Undefined array key "usage"
Filename: controllers/Detail.php
Line Number: 258
Backtrace:
File: /var/www/html/application/controllers/Detail.php
Line: 258
Function: _error_handler
File: /var/www/html/index.php
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Function: require_once
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Message: Trying to access array offset on value of type null
Filename: controllers/Detail.php
Line Number: 258
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File: /var/www/html/application/controllers/Detail.php
Line: 258
Function: _error_handler
File: /var/www/html/index.php
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Function: require_once
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Message: Undefined array key "usage"
Filename: controllers/Detail.php
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Function: _error_handler
File: /var/www/html/index.php
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Filename: controllers/Detail.php
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Function: _error_handler
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Filename: controllers/Detail.php
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File: /var/www/html/application/controllers/Detail.php
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Function: _error_handler
File: /var/www/html/index.php
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Filename: controllers/Detail.php
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Function: _error_handler
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Filename: controllers/Detail.php
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Function: _error_handler
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Function: require_once
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Message: file_get_contents(https://...@gmail.com&api_key=61f08fa0b96a73de8c900d749fcb997acc09): Failed to open stream: HTTP request failed! HTTP/1.1 429 Too Many Requests
Filename: helpers/my_audit_helper.php
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File: /var/www/html/application/helpers/my_audit_helper.php
Line: 143
Function: file_get_contents
File: /var/www/html/application/helpers/my_audit_helper.php
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Function: simplexml_load_file_from_url
File: /var/www/html/application/helpers/my_audit_helper.php
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Function: getPubMedXML
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Function: pubMedSearch_Global
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Function: pubMedGetRelatedKeyword
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Filename: helpers/my_audit_helper.php
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File: /var/www/html/application/helpers/my_audit_helper.php
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File: /var/www/html/application/controllers/Detail.php
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Function: pubMedGetRelatedKeyword
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Function: require_once
A kinetic Monte Carlo (kMC) simulation algorithm is developed for computing the effective diffusivity of water molecules in a poly(methyl methacrylate) (PMMA) matrix containing carbon nanotubes (CNTs) at several loadings. The simulations are conducted on a cubic lattice to the bonds of which rate constants are assigned governing the elementary jump events of water molecules from one lattice site to another. Lattice sites belonging to PMMA domains of the membrane are assigned different rates than lattice sites belonging to CNT domains. Values of these two rate constants are extracted from available numerical data for water diffusivity within a PMMA matrix and a CNT pre-computed on the basis of independent atomistic molecular dynamics simulations, which show that water diffusivity in CNTs is 3 orders of magnitude faster than in PMMA. Our discrete-space, continuum-time kMC simulation results for several PMMA-CNT nanocomposite membranes (characterized by different values of CNT length L and diameter D and by different loadings of the matrix in CNTs) demonstrate that the overall or effective diffusivity, D(eff), of water in the entire polymeric membrane is of the same order of magnitude as its diffusivity in PMMA domains and increases only linearly with the concentration C (vol. %) in nanotubes. For a constant value of the concentration C, D(eff) is found to vary practically linearly also with the CNT aspect ratio L/D. The kMC data allow us to propose a simple bilinear expression for D(eff) as a function of C and L/D that can describe the numerical data for water mobility in the membrane extremely accurately. Additional simulations with two different CNT configurations (completely random versus aligned) show that CNT orientation in the polymeric matrix has only a minor effect on D(eff) (as long as CNTs do not fully penetrate the membrane). We have also extensively analyzed and quantified sublinear (anomalous) diffusive phenomena over small to moderate times and correlated them with the time needed for penetrant water molecules to explore the available large, fast-diffusing CNT pores before Fickian diffusion is reached.
Download full-text PDF |
Source |
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http://dx.doi.org/10.1063/1.4934225 | DOI Listing |
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