I am generating a square wave with a 555 timer chip and I am trying to obtain a triangle wave from the 555's output by using an op-amp (LM324N) as an integrator. The op-amp is in single power supply mode with pin 4 (V+) connected to Vcc (+5V) and pin 11 (GND) connected to GND. At first I thought it might be because I am saturating the op-amp's inputs, but then I measured the 555 output with a digital multimeter and it indicates that when the 555 OUTPUT goes HIGH it puts out about 3.5 V. In the initial configuration (blue in the drawing) the LED1 pulses as it should along with the 555 OUTPUT but the LED2 (op-amp output) is constantly off.
Then I inversed the polarity of the LED and wired it to Vcc instead of GND (as seen in red) and it stays always on, regardless of 555 output.
The Op amp inverting input is connected via a 220ohm resistor to 555 OUTPUT and via a 10 nanoFarad capacitor to op-amp's output (pin 1), the non-inverting input (pin 3) is connected to ground.
What am I doing wrong here? And how can I get a triangle wave with an op amp from the square wave output?